PURPOSE: To reduce the generation of a H2S odor, by forming a catalyst for purifying exhaust gas by supporting metal oxide such as activated alumina by a carrier and further supporting a metal selected from Pt, Rh and Pd or oxide thereof by said carrier.

CONSTITUTION: At least one oxide of a metal selected from a group consisting of titanium, niobium, vanadium, tantalum and manganese is used other than activated alumina, cerium oxide and an alumina sol, and all of them are mixed and ground to prepare a slurry. After a carrier is immersed in this slurry, the impregnated carrier is dried and baked to form a film composed of composite oxide or an oxide mixture on the carrier. Subsequently, at least one catalytic metal selected from a group consisting of platinum, rhodium and palladium is supported by the film on the carrier to prepare a catalyst for purifying exhaust gas. This catalyst has high exhaust gas purifying efficiency and reduces the discharge of H2S from exhaust gas after long-time used.